Chirped bragg grating elements

ABSTRACT

Apparatus and methods for altering one or more spectral, spatial, or temporal characteristics of a light-emitting device are disclosed. Generally, such apparatus may include a volume Bragg grating (VBG) element that receives input light generated by a light-emitting device, conditions one or more characteristics of the input light, and causes the light-emitting device to generate light having the one or more characteristics of the conditioned light.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a division of U.S. patent application Ser. No.10/884,524, filed Jul. 2, 2004 now U.S. Pat. No. 7,298,771, which claimsbenefit under 35 U.S.C. § 119(e) of provisional U.S. patent applicationsNos. 60/484,857, filed Jul. 03, 2003, and 60/564,526, filed Apr. 22,2004. The respective disclosures of each of the above-referenced patentapplications are incorporated herein by reference.

FIELD OF THE INVENTION

The invention is related generally to light emitting devices, such aslasers, laser diodes, light-emitting diodes, super-luminescent laserdiodes, etc. More specifically, the invention provides for using one ormore volume Bragg grating (VBG) elements for modifying (or conditioning)one or more output characteristics of such devices.

BACKGROUND OF THE INVENTION

Laser cavities or resonators, however complex, typically include two ormore mirrors or other reflecting devices that form a closed optical pathfor rays traveling in a certain direction. An optical element positionedin that closed optical path, which includes mirrors and/or otherreflecting devices that form the path, may be referred to as“intra-cavity.” An optical element positioned in the path of light thathas departed from the resonator may be referred to as an “extra-cavity”element.

Using extra-cavity partial reflectors as feedback elements with asolitary laser cavity has been attempted in the past with a purpose ofachieving single longitudinal mode operation of the otherwise multi-modelaser. Such reflectors, however, were not wavelength-selective devices.Such designs may be referred to as the “coupled-cavity” approach. Thisapproach suffered from instabilities stemming from the non-selectivenature of the feedback.

Another approach used was to employ a dispersive element, such assurface diffraction grating, as an extra- or intra-cavitywavelength-selective device in order to induce narrow-band or singlelongitudinal mode operation of a semiconductor laser. Althoughsuccessful in a laboratory, this approach results in rather bulkydevices, which are difficult to align and to maintain in the field.

A somewhat more practical approach for inducing narrowband operation ofa single-transverse mode semiconductor laser proved to be a fiber Bragggrating functioning typically as an extra-cavity element. This device isa narrow-band reflector that functions only in an optical fiberwaveguide. It is, therefore, inapplicable to solid-state lasers, laserdiode arrays, and, most likely, even to multi-mode (transverse)broad-area high-power single-emitter laser diodes, whether fiber-coupledor not.

The use of a volume Bragg grating element has been suggested as anintra-cavity element to induce single-longitudinal mode (also calledsingle-frequency) operation of a single-transverse mode laser diode. Inthis approach, the volume Bragg grating element forms the external Braggmirror of an external-cavity single-spatial mode semiconductor laserdiode. However, to the inventors' knowledge, neither the possibility ofusing a VBG element for extra-cavity narrow-band feedback nor apractical device for achieving narrow-band operation of asingle-transverse mode semiconductor laser diodes have been disclosedpreviously. Furthermore, to the inventors' knowledge, not even thepossibility of applying VBG elements to multiple-transverse mode,broad-area laser diodes, laser diode arrays or the possibility ofconditioning other attributes of laser emission (such as its spatialmode and temporal profile) have been disclosed previously.

To the inventors' knowledge, there are currently no devices in themarket that employ volume Bragg grating elements for conditioning oflaser characteristics, nor are there any successful practical devices inthe market that use any of the above-mentioned approaches to improve theoutput characteristics of arrays of lasers.

SUMMARY OF THE INVENTION

The invention provides methods and apparatuses that can overcome theproblems known in the prior art. The invention provides severalpractical embodiments of using VBG elements for conditioning any or allof the output characteristics of lasers and other light-emittingdevices.

The inventors have found that volume Bragg grating (VBG) elementsrecorded in photorefractive materials, particularly those recorded ininorganic photorefractive glasses (PRGs), have many properties that canimprove one or more characteristics of light-emitting devices such assolid-state lasers, semiconductor laser diodes, gas and ion lasers, andthe like. A volume Bragg grating (“VBG”) element may be any structurethat: a) has a periodically varying index of refraction in its bulk (theshape of the surface of the constant index of refraction can be anysmooth figure, flat or curved); b) is generally transparent in thespectral region of its operation; and c) has a thickness in thedirection of propagation of light of 0.05 mm or more.

A photorefractive material may include any material that has the abilityto change its index of refraction subsequent to illumination by light ofcertain wavelength region or regions. Such a change in refractive indexmay occur in the material either immediately upon illumination by lightor as a result of secondary processing step or steps, whether chemical,thermal, etc. Such a material may also be generally transparent in thespectral region of its photosensitivity, i.e. the light at the recordingwavelength may have the ability to penetrate sufficiently deep into thematerial (>0.1 mm) without suffering excessive absorption (>90%).Further, the material may be amorphous and generally isotropic.

Though the embodiments described herein are directed to certain examplesof laser devices, it should be understood that the principles of theinvention apply to other light-emitting devices as well. For example,applications of this invention include but are not limited to:high-power, semiconductor, solid state, ion, and gas lasers;light-emitting diodes and super-luminescent laser diodes; medicaldiagnostics, treatment, and surgical instruments; environmental sensors;metrology instruments; industrial applications; and defenseapplications.

Properties of VBG elements, and methods for manufacturing VBG elements,have been described previously (see, for example, U.S. patentapplication Ser. No. 10/390,521, filed Mar. 17, 2003).

Generally, there are at least three distinct characteristics of theoutput of a laser device that may be improved using the techniques ofthe invention: 1) emission spectrum (e.g., peak wavelength of the laseremission and its spectral width); 2) spatial/angular beamcharacteristics (e.g., the angular divergence of the output laser beamand its spatial mode structure); and 3) temporal profile of the laserpulses (e.g., the duration of the laser pulse, its temporal phasevariation or chirp etc.). As used herein, spectral, spatial, or temporalconditioning, refer to affecting any of the above characteristics,respectively.

The inventors have found that VBG elements permanently recorded in asuitable material, particularly a PRG, have a number of properties thatcan be utilized for improving one or more of the above characteristics.These properties include, but are not limited to: 1) single spectralpass band without any extraneous pass bands; 2) ability to control thespectral width of the VBG filter pass band; 3) ability to control theamplitude and phase envelope of a VBG filter; 4) narrow acceptance anglerange otherwise called field of view; 5) ability to control theacceptance angle and the field of view; 6) ability to multiplex morethan one filter in the same volume of the material; 7) high damagethreshold of the VBG elements manufactured in a suitable material,particularly PRG; 8) ability to be shaped into bulk optical elementswith sufficiently large clear aperture; and 9) reflectivity distributedover the volume of the material.

The invention provides apparatus and methods by which these propertiesof VBGs may be applied to the improvement of the above-mentioned lasercharacteristics.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-1C depict a VBG as an extra-cavity element for wavelengthlocking by self-seeding; FIG. 1D provides plots of wavelengthcharacteristics with and without laser conditioning.

FIGS. 2A and 2B depict wavelength locking by use of a transmission VBG.

FIG. 3 depicts a wavelength stabilization concept for a high-power laserbar.

FIGS. 4A and 4B depict wavelength locking by self-seeding for amulti-mode laser diode bar.

FIG. 5 depicts locking of a laser diode array by use of a hybrid elementcombining the fast axis collimating lens and a VBG.

FIG. 6 depicts wavelength locking of laser diode stacks.

FIG. 7 depicts laser wavelength stabilization by self-seeding through aback-facet.

FIG. 8 depicts a wavelength-shifted laser diode bar/stack.

FIG. 9 depicts wavelength multiplexing of the output of awavelength-shifted laser diode bar/stack for higher brightness.

FIG. 10 depicts a VBG mirror forming part of a laser cavity.

FIG. 11 depicts using a VBG for a single longitudinal laser modeselection.

FIGS. 12A and 12B depict using a VBG element for selection of a singlelongitudinal mode of a laser in distributed feedback configurations.

FIG. 13 depicts spatial mode stripping by use of a VBG.

FIGS. 14A-14D depict examples of various angular diffraction efficiencyprofiles of VBG elements for spatial mode stripping in non-foldingconfigurations.

FIG. 15 depicts simultaneous single longitudinal mode and TEM₀₀ modeselection by use of VBG element with smoothly varying reflectivityprofile.

FIG. 16 depicts conditioning of the temporal profile of pulsed lasers.

FIGS. 17A-17C depict how a VBG may be used to construct tunable devices.

FIGS. 18A and 18B depict simultaneous spectral and spatial conditioning,and combining of the output of an array of emitters by use of anexternal feedback filtered through a wavelength multiplexing device.

FIG. 19 depicts the results of spectral conditioning of laser diodes byuse of VBG in extra-cavity configuration.

FIG. 20 depicts the output power characteristics of a laser diode lockedby an external VBG element.

FIG. 21 depicts the results on the improvement in thermal drift of alaser diode locked by an external VBG element.

FIG. 22 depicts the results in improving spatial characteristics of alaser diode locked by an external VBG element.

FIGS. 23A and 23B depict an embodiment for extra-cavity doubling of ahigh-power laser diode frequency.

FIGS. 24A-24C depict another embodiment for extra-cavity doubling of ahigh-power laser diode frequency.

FIGS. 25A and 25B depict intra-cavity doubling of a high-power laserdiode frequency.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

Overview

There are at least two general approaches to using VBG elements forconditioning a characteristic of a light emitting device: a) using a VBGthat is outside of the laser cavity (extra-cavity); and b) using a VBGthat is inside laser cavity (intra-cavity).

As discussed above, a laser resonator may be viewed as a closed opticalpath formed between mirrors and/or other light-reflecting elements. Sucha closed optical path is typically a condition that is necessary forlasing to occur. For this reason, it is desirable that any intra-cavityelement added to the resonator does not alter this condition, lest itimpede light generation via stimulated emission. By contrast tointra-cavity elements, extra-cavity elements may be free from such aconstraint. Furthermore, the efficiency of light generation typicallydepends nonlinearly on single-pass cavity loss. Thus, it is alsodesirable that any intra-cavity element used for laser outputconditioning have as little loss as possible. This includes the lossesin the element itself, as well as the losses in the optical deliverysystem used to project light onto the element and back. In contrast,extra-cavity elements used for laser output conditioning may be muchmore tolerant to the loss factor.

When used for narrowing the spectral output of a laser, intra-cavityelements provide wavelength-selective loss that raises the lasingthreshold for all but a few cavity modes. In contrast, the feedback froman extra-cavity wavelength-selective element reduces lasing thresholdfor just a few cavity modes, which creates preferred lasing conditionsfor those modes. These modes, then, consume most or all of the availablelaser gain and prevent other modes from lasing. Similar processes affectthe formation of the spatial mode of the laser when intra- andextra-cavity elements are used for spatial mode conditioning.

An optical delivery system may be viewed as a collection of opticalelements, e.g. lenses, mirrors, prisms etc., that collects some or allof the light emanating from a particular aperture of the laser cavity,projects some or all of this light onto a VBG element or a systemthereof, and then collects some or all of the light returned from saidVBG element and projects it back onto the aperture of laser cavity.

When considering the intra-cavity use of VBG elements, a design factorthat may be considered is the reduction of the total loss of the VBGelement plus the optical delivery system for the preferred longitudinaland transverse modes of the laser. In comparison, the design of anextra-cavity system for laser output conditioning may be more complex.In order to achieve stable output with desired characteristics, it maybe desirable to optimize any or all of the following factors: 1) Thesolitary cavity design, including, but not limited to, cavity length,reflectivity of the cavity mirrors, threshold, differential efficiency,etc., all of which may be dependent on the properties of the gainmedium; 2) The intrinsic reflectivity and loss of the VBG element; 3)The spectral bandwidth of the VBG element; 4) The reflectivity of theVBG element facets; 5) The relative angle between the volume Bragggrating planes and the external facets of the element; 6) The design ofthe external optical delivery system projecting light onto and back fromthe VBG element, including, but not limited to, its total couplingefficiency into the solitary laser cavity, the length of the externalcavity, the divergence of the light (in both directions) incident uponthe VBG and the output coupler of the solitary cavity, etc.

For example, single-transverse mode laser diodes that are stabilized bya fiber Bragg grating may have such a fiber Bragg grating positionedrather far from the laser diode chip (typically about 1 meter) in orderto induce the so-called coherence collapse regime of operation. Such acondition may be necessary to achieve stable laser output. However, if aVBG element was used as a mere free-space replacement of the fiber Bragggrating, it may result in a device 1.5 m long without an advantage ofeasy coiling or folding that the optical fiber affords naturally. Such adevice might not be practical, however, and, therefore, different stableoperating conditions might be desirable for devices using VBG elementsfor laser output conditioning, which are the result of the optimizationof the above-described parameters.

Extra-Cavity Use of VBG Elements

A VBG element may be used extra-cavity to condition, spectrally,spatially, and/or temporally, light received from a light-emittingdevice. At least a portion of the conditioned light may then be fed backinto the laser cavity. In the process of doing so, the light emittedfrom the laser will assume the characteristics of the light conditionedby the VBG. Example embodiments of such extra-cavity use of VBG elementsare depicted in FIGS. 1-9. Note that, when the VBG is used inextra-cavity configuration, the laser device is operating abovethreshold in the absence of optical feedback from the VBG element.

In an example embodiment, a VBG element and a laser output coupler maybe positioned in conjugate planes. An optical system including one ormore lenses may be positioned in the light path after the light exitsthe laser cavity through the output coupler. Such an optical system mayform an image of the output coupler in a particular location in spaceoutside the laser cavity. A VBG element may be positioned in that planeso that the VBG element reflects the light rays incident upon it in suchfashion that the reflected rays go back through the imaging opticalsystem and form an image in the plane of the output coupler. In thiscase, it may be said that the output coupler and the VBG are positionedin the conjugate planes of the imaging optical system. A feature of thisconfiguration is that it maximizes the coupling efficiency from theexternal element (the VBG element in this case) back into the lasercavity, essentially matching the resonator mode pattern in bothtransverse directions. Such an embodiment may be desirable where thelaser cavity is a waveguide, such as in the case of semiconductor laserdiodes, for example.

In another example embodiment, the output of a waveguide laser cavity(e.g., a semiconductor laser diode) may be approximately collimated inone axis (e.g., the fast axis) by a cylindrical lens. The other axis(e.g., the slow axis) of the laser output may be allowed to divergefreely. The VBG element may be positioned in the optical path of thelaser output behind the cylindrical lens and aligned in such a way thatit reflects portion of the laser light back into the laser cavity. Inthis embodiment the coupling efficiency of the optical delivery system(e.g., the cylindrical lens) from the VBG back into the laser cavity isvery low, making it undesirable for use as an intra-cavity element.However, such a system may be designed to operate stably in anextra-cavity configuration. It will induce wavelength-stable, spectrallynarrowed operation of the laser diode. In this configuration thedivergence of the non-collimated laser axis (the slow axis) can also bereduced without the use of additional optics, when such a laser is abroad-area multiple transverse mode semiconductor laser diode. In thisconfiguration an entire linear array of semiconductor lasers can beconditioned with a single cylindrical lens and a single VBG element.

An example embodiment of a broad-area high-power semiconductor laser,having an emitting aperture of greater than about 50 μm, with outputconditioned by an extra-cavity VBG with a cylindrical fast-axis lens, isalso disclosed. The output power of the laser changes ratherinsignificantly despite the fact that the VBG reflectivity is relativelyhigh (30%). Small reduction in the output power is a factor in thedesign of practical systems using high-power laser diodes and may beprovided by the invention.

Example design parameters for stable operation of broad-areasemiconductor laser diodes may include: laser cavity, 1-3 mm long;emitting aperture, 100-500 μm; back facet reflectivity, 0.9 or greater;front facet reflectivity, 0.5-20%; FAC lens EFL, 50-2000 μm; FAC lenstype, graded-index cylindrical or plano-convex aspheric cylindrical; FACAR coating, all facets <2%; VBG reflectivity, 5-60%; VBG thickness,0.2-3 mm; VBG position behind FAC lens, 0-10 mm; and angle of the VBGplanes with respect to its facet, 0-5 degrees.

An example embodiment of an extra-cavity VBG without any opticaldelivery system (e.g., without any lenses) is also disclosed. In thisembodiment a VBG element may be positioned in the optical path of thelight behind the output coupler (e.g., the laser diode front facet)without any extra optical elements (e.g., lenses) in between. In thecase of a waveguide cavity, such as the case for semiconductor laserdiodes, only a very small portion of the total laser output power may bereturned by the VBG into the laser cavity. However, with proper lasercavity and VBG design, it is possible to achieve spectral narrowing andstabilization of the output wavelength across a range of operatingconditions.

Example design parameters for such an embodiment may include: lasercavity, 1-3 mm long; emitting aperture, 100-500 μm; back facetreflectivity, 0.9 or greater; front facet reflectivity, 0.2-5%; VBGreflectivity, 30-99%; VBG thickness, 0.05-3 mm; VBG position in front ofthe laser, 0-5 mm; and angle of the VBG planes with respect to itsfacet, 0-5 degrees.

Some of the embodiments described herein demonstrate how the output of alaser diode, laser diode bar, or stack may be modified spectrally and/orspatially. Effects of the VBG element in these cases include spectralnarrowing of the emission line of a laser or laser array, stabilizationof the peak emission wavelength of a laser or a laser array, and thereduction of the divergence of the slow axis of a laser or a laserarray.

Note that the high total output power of the laser transmitting throughthe clear aperture of the VBG (>20 W for laser diode arrays), the highpower density on the VBG element (>40 W/cm²) as well as high temperatureexcursions suffered by such an element (T>100 C) may limit the choice ofsuitable materials for VBG implementation. Nevertheless, the inventorshave successfully demonstrated VBG elements operation in all of theabove conditions when implemented in PRG materials.

FIG. 8, for example, demonstrates how both of these properties may beutilized in order to combine the output of an entire array of lasersonto a single target using a single VBG. In that embodiment, the VBGelement contains a grating having a period that varies depending onlocation. When positioned properly in front of an array of emitters,such a grating will force different emitters to operate at a differentpeak wavelength depending on their location, creating awavelength-shifted laser array. The output of such an array may besubsequently combined by use of one of a number of well-known wavelengthmultiplexing techniques into a much brighter spot with intensityessentially equivalent to that of the entire array and spatialdimensions essentially equivalent to that of an individual emitter.

An embodiment for spectral power combining of a laser diode array viaexternal feedback through a wavelength multiplexer is also disclosed. Inthis embodiment, a wavelength multiplexer may be positioned in the pathof output light of an array of emitters and behind an optical deliverysystem. Such a multiplexer may be designed to combine the output of allthe emitters into one beam, provided they operate at the wavelengthsmatching the appropriate input channels of the multiplexer. Such acondition may be achieved automatically when an external feedback isprovided into the emitters from a partial reflector positioned in thelight path behind the wavelength multiplexer. In this configuration, thereflected light will travel back through the multiplexer and separateinto multiple channels different in wavelength. As a result, each of theemitters in the array will receive feedback at a wavelength matchingthat of the corresponding channel of the multiplexer. Such feedback willforce each emitter to operate at appropriate wavelength, so that theiroutput power is efficiently combined.

Other applications include, but are not limited to, stabilization ofsuper-luminescent laser diodes, light-emitting diodes, solid-statelasers, gas and ion lasers; wavelength stabilization of sources used intelecommunications, sensing, metrology, material processing, otherindustrial applications and defense electronics; multi-wavelengthemitters and emitter arrays for use in any of the application areasmentioned above; and tunable-wavelength emitters.

Intra-Cavity Use of VBG Elements

VBG elements may be used inside a laser cavity, rather than through anexternal feedback, to affect laser output directly. Examples ofembodiments of intra-cavity use of VBG elements are provided in FIGS.10-16.

A VBG may be used to force a laser to operate on a single longitudinalmode. Due to the highly selective reflectivity of a VBG reflector, onlyone longitudinal mode of the laser cavity has gain exceeding the lasingthreshold. Conventionally, monolithic or air-spaced etalons are used toselect a single longitudinal mode of a solid-state laser (e.g., Nd:YAG).Very often, additional elements (e.g., thin etalon or a birefringentfilter or both) are employed in order to achieve single-frequencyoperation, even for a narrow gain-bandwidth medium. It may be desirablethat these elements, which provide wavelength-selective loss inside thecavity, are tuned in synch with each other and with the length of themain cavity in order to provide continuous, hop-free tuning.

There are numerous ways to achieve single longitudinal mode (or singlefrequency) operation, with some of the embodiments described below. Inone embodiment, a reflective VBG element may be used as the outputcoupler or the high reflector of a laser resonator. The length of theVBG element may be selected in such a way that its reflectivity dropsrapidly when the wavelength is detuned from the Bragg condition.Consequently, only one resonator mode reaches lasing threshold.

In another embodiment, two VBG elements may be employed—one as the highreflector and one as an output coupler of the laser resonator. The VBGelements may have slightly shifted peak reflectivity wavelengths, whichcreates more rapid change in cavity loss with wavelength. This wouldallow the use of shorter, less selective VBG elements and/or longerlaser resonators.

In yet another embodiment, the VBG may act as a distributed feedback(DFB) element, taking place of both resonator mirrors. Such an elementmay be monolithic, with proper phase shift between the two halves of theBragg grating. In this embodiment, the active medium may be the VBGitself, which can be achieved with proper doping with active ions, orthe active medium can be attached to the VBG element along the length ofthe Bragg grating, partially or entirely.

It may be desirable that a laser output include only one (e.g., thelowest) spatial mode, which in free-space resonators has the designationTEM₀₀. This mode has a smooth intensity profile and the lowest possibleangular divergence. However, such TEM₀₀ operation is often ratherdifficult to achieve in high-power lasers with high single-pass gain.The techniques for achieving TEM₀₀ operation usually rely on thedifferences in the spatial and angular profile of the TEM₀₀ and thehigher modes by introducing an element or elements withposition-dependent loss (apertures) or angle-dependent loss. VBGs arewell suited to serve in either capacity.

Glebov, et al., have disclosed an approach for using a transmission-typeVBG element inside a solid-state laser cavity to provide anangle-dependent cavity loss. However, that approach uses a VBG as anintra-cavity folding element that has very high angular sensitivity andrequires very delicate and extremely accurate alignment. If thealignment of such a folding element is disturbed, the laser generationwill seize, which makes this approach undesirable. A preferred approachwould be to use a mode-forming element that by itself does not requirecritical alignment and, when perturbed, would not stop laser operation,but rather allow higher spatial modes to achieve lasing threshold, atmost. This requires an element or elements that have low loss for TEM₀₀mode, have high loss for all higher modes, and do not alter the opticalpath of the TEM₀₀ mode. This class of intra-cavity mode-forming elementsmay be referred to as “non-folding” mode-forming or mode-strippingelements.

It should be understood that the diffraction efficiency of a VBG elementdepends on the angle of incidence for a given wavelength of light. Forthis reason, it will produce an angle-dependent gain/loss profile in thelaser cavity. Such a gain profile will create higher losses for spatialmodes higher than TEM₀₀ and, therefore, can be used for suppressinghigher spatial mode in the laser resonator (“mode-stripping”), resultingin a clean TEM₀₀ output of the laser.

To function as a spatial mode-stripping device, a VBG element may have avariety of angular diffraction efficiency profiles, such as thoseprovided and described below in connection with FIG. 12. It should beunderstood that other possible types of angular profiles of diffractionefficiency of a VBG element may lead to the desired effects on theoutput of a laser. It should also be understood that reflection andtransmission type VBG elements, as well as hybrid elements, may beutilized to achieve the desired effect. The principles of the inventionmay be applied to any or all of these cases without limitation.

An example embodiment of a non-folding mode-forming element is a VBGmirror with a Gaussian or super-Gaussian reflectivity profile. In thisembodiment, a reflective VBG element may have an axially-symmetricreflectivity profile with smooth radial variation of the reflectivityfollowing, preferably, a super-Gaussian shape. Such an element, whenused either as an output coupler or the high reflector of the lasercavity, may be designed to overlap spatially with the TEM₀₀ mode at thatparticular location within the resonator, but it would have high lossesfor all the higher resonator modes. Such a VBG element with a softaperture may have either plane parallel Bragg planes (e.g., a zerooptical power VBG element) or have Bragg planes designed to have aparticular curvature (e.g., a VBG element with finite optical power).

Another embodiment includes the use of a transmissive, non-folding VBGelement to diffract higher resonator modes away from the resonatoroptical axis. This approach relies on the high angular selectivity ofthe transmissive VBGs and may be made with such angular reflectivityprofile that the TEM₀₀ mode is transmitted through such an elementwithout being diffracted, that is, with little or no loss. Several orall of the higher modes, starting with TEM₀₁/TEM₁₀, may experiencesufficient diffraction, and, therefore, loss, such that they do notreach the threshold for lasing. Such a VBG element may or may not haveaxial symmetry in its angular profile of the diffraction efficiency.

Yet another example embodiment is based on the natural angularselectivity of a reflective VBG. Such a VBG element, serving as theoutput coupler or the high reflector of the laser cavity, would havehigh reflectivity for the incident waves of a particular wavelength nearthe normal to the grating planes, but the reflectivity would droprapidly for the waves incident upon such VBG element at an angle outsideits angular acceptance. Therefore, the VBG element would satisfy thethree criteria for non-folding mode-forming elements outlined above.

The amplitude and phase envelope of the VBG may be adjusted in order toproduce a desired effect on the temporal profile of ultra-short laserpulses. One particular example is the compensation of pulse chirpingproduced inside the laser cavity by other elements, such as the lasergain medium.

DETAILED DESCRIPTIONS OF EXAMPLE EMBODIMENTS DEPICTED IN THE FIGURES

FIGS. 1A-C illustrate applications of a VBG as an extra-cavity elementfor wavelength locking via self-seeding, that is, where the VBG elementprovides wavelength-selective feedback into the laser cavity. FIG. 1Ashows wavelength locking and narrowing by use of an optical deliverysystem 104. Laser radiation 102 is emitted from the emitting aperture ofa laser 100. The optical delivery system 104 redirects the emittedradiation 102, as a redirected emission 105, onto a VBG element 106.Radiation 107 is reflected by the VBG element 106. The optical deliverysystem 104 redirects the reflected radiation 107, as redirectedreflected radiation 103, back onto the emitting aperture of the laser100. The redirected reflected radiation 103 acts as a narrow-wavelengthseed, forcing the laser 100 to operate at the wavelength of the VBG 106and also narrowing its emission spectrum.

As shown in FIG. 1B, laser radiation 112 is emitted from the emittingaperture of a laser 110. An optical delivery system 114 collimates theemitted radiation 102, as collimated radiation 115, onto a VBG element116. The VBG element 116, having a narrow-wavelength reflectance,reflects at least a portion 117 of the laser energy back through theoptical delivery system 114 and into the laser cavity of the laser 110.The reflected radiation 117 acts as a narrow-wavelength seed, forcingthe laser 110 to operate at the wavelength of the VBG 116 and alsonarrowing its emission spectrum.

FIG. 1C shows wavelength locking by a VBG element without an opticaldelivery system. As shown, laser radiation 122 is emitted from theemitting aperture of a laser 120 and is incident onto a VBG element 126.The VBG element 126, having a narrow-wavelength reflectance, reflects atleast a portion 127 of the laser energy back into the laser cavity ofthe laser 120. The reflected radiation 127 acts as a narrow-wavelengthseed, forcing the laser 120 to operate at the wavelength of the VBG 126and also narrowing its emission spectrum.

FIG. 1D provides plots of wavelength characteristics with and withoutlaser conditioning. As shown, the conditioned radiation (e.g., radiation103, 117, 127) has a bandwidth, b₂, that is much more narrow than thebandwidth, b₁, of the unconditioned radiation (e.g., radiation 102, 112,122). Also, the peak intensity I₂ of the conditioned radiation isgreater than the peak intensity I₁ of the unconditioned radiation.

FIGS. 2A and 2B illustrate wavelength locking using an extra-cavitytransmission VBG. The light 132 emitted by a laser 130 may be collimatedby a lens 134 and is incident upon a VBG 136. The portion 135 of thelight 132 having a wavelength within the passband of the VBG 136 isdiffracted by the VBG 136, deflected from its original path. Thediffracted light 135 is incident upon a reflective surface 138, whichmay be formed on the VBG element itself, as shown in FIG. 2A, orprovided as an external element, as shown in FIG. 2B. Upon beingreflected by the surface 138, the reflected diffracted light 139 isredirected by the VBG element 136, as redirected light 137 back throughthe lens 134 and into the laser cavity of the laser 130. Thus, the laser130 may be forced to operate at a wavelength determined by the VBG 136.

FIG. 3 depicts the output of a laser diode bar 140 locked by a singleVBG element 146 using a single micro-lens 144. The radiation output bythe laser diode bar 140 may be collimated on an axis (say, the y-axis asshown in FIG. 3) by the micro-lens 144, which may be a cylindrical lens,for example, and is incident upon the VBG element 146. The VBG element146, which may have generally the same grating period through its entirevolume, reflects at least a portion of the light back into the cavitiesof the individual emitters 141 in the bar 140. The effect produced onthe output of the emitter array is essentially the same as on anindividual emitter. As a result, the output of the entire bar 140 islocked to one wavelength determined by the VBG element 146.

FIGS. 4A and 4B illustrate the use of a cylindrical lens 144 for lockinga bar 140 of multimode laser diodes 141. FIG. 4A shows a cross-sectionof the laser diode bar 140. The light emitted by the laser bar 140 maybe collimated or reduced in divergence on the fast axis (y-axis as shownin FIG. 3) by the cylindrical lens 142 and is incident upon the VBGelement 146. The VBG element 146 reflects some light back into the lasercavity. FIG. 4B shows the top view of the laser diode bar 140. The lightemitted by the individual emitters 141 in the diode bar 140 is incidentupon the cylindrical lens 142. The slow axis of the emitted light coneis not collimated. It is subsequently incident upon the VBG element andis reflected back onto the face of the diode bar.

FIG. 5 shows how a hybrid optical element 148, which may be a combinedlens and VBG element, can be used for conditioning of an entire array140 of emitters 141. The lens portion 146 of the hybrid optical element148 can be formed directly on the surface of the VBG element 144 orseamlessly fused onto it.

FIG. 6 shows the concept of locking a stack 150 of diode bars 151. Thereare several diode bars 152 in the stack 150, each of which includes aplurality of individual emitters 151 exposed at the face of the stack150. The light emerging from the individual emitters 151 may becollimated by a set of cylindrical micro-lenses 154. Preferably, arespective lens 154 is provided for each diode bar 152 (though it shouldbe understood that other lens arrangements may be used as well). Thelenses 154 collimate the fast axes of the bars 152 and the emitted lightsubsequently enters the VBG element 156. The VBG element 156 may haveessentially the same period grating through its entire volume. The VBGelement 156 reflects at least a portion of the incident light backthrough the lenses 154 onto the face of the stack 150, with at least aportion of the reflected light entering the cavities of the individualemitters 151. The result is that the output of the entire stack 150 islocked to the same wavelength determined by the VBG element 156.

FIG. 7 depicts locking a light emitter 160 by placing a VBG element 166behind the back facet of the emitter 160. The back facet of the emitter160 is partially transmissive to light. The light exiting that facet iscollimated by an optical delivery system (e.g., a lens) 164 and then isincident upon the VBG element 166. The VBG element 166 reflects at leasta portion of this light back onto the back facet of the emitter 160,with at least a portion of the reflected light entering the laser cavityof the emitter 160. This results in locking the wavelength of theemitter 160 to that of the VBG element 166.

FIG. 8 depicts producing an array of emitters with different wavelengthoutputs. This concept may be applied to either one- or two-dimensionalarrays. All the emitters 171 in the array 170 may be made from the samematerial, and, therefore, may have essentially the same natural outputwavelength. The light emerging from the individual diode bars 172 in thestack 170 may be collimated by a set of cylindrical micro-lenses 174.Preferably, a respective lens 174 is provided for each diode bar 172(though it should be understood that other lens arrangements may be usedas well). The lenses 174 collimate the fast axes of the bars 172 and theemitted light subsequently enters the VBG element 176. The gratingperiod of the VBG element 176 may differ depending on the location alongthe grating coordinate parallel to the laser bar(s) 172. The VBG element176 reflects at least a portion of the incident light back onto the faceof the stack 170, and at least a portion of the reflected light entersthe cavities of the individual emitters 171. As a result, the emittingwavelength of the individual laser diodes 171 in the bar(s) 172 may belocked to different values depending on the location of the emitters 171relative to the VBG 176.

FIG. 9 depicts wavelength multiplexing of the output of thewavelength-shifted laser diode bar/stack 170 described in FIG. 8 toproduce a higher brightness light source. The output of an array ofemitters 170 is conditioned by a lens or lens array 174 and subsequentlyenters a VBG element 178. The VBG element 178 has a grating period thatmay vary depending on the location along the grating coordinate parallelto the array of the emitters 170. The VBG element 178 thus forces theindividual emitters to operate at different wavelengths depending on thelocation within the array.

The output of such a wavelength-shifted emitter array may be directedinto a wavelength multiplexer 180 capable of multiplexing differentwavelengths of light into a single output. Such a multiplexer 180 may beconstructed using any of a number of well-established techniques,including, but not limited to diffraction gratings, VBG elements,thin-film dielectric filters, arrayed-waveguide grating(s), or any otheroptical elements or a combination of optical elements capable ofdelivering this basic function. The output of the entire emitter array170 may thus be combined into a single spot with essentially all opticalpower of the entire array concentrated in one spot on a target (notshown), which can be or include, without limitation, an optical fiber,optical fiber array, detector, detector array, emitter, emitter array,solid-state material that needs to be processed (e.g., cut, welded,melted, etc.), liquid, gas, or the like.

FIG. 10 depicts a VBG element 202 inside a laser cavity 200. The lasercavity 200 may include one or more mirrors 208 (back facet, as shown, orfront facet, not shown), a gain medium 206, conditioning optics 204, anda VBG element 202. Preferably, the gain medium 206 may be or include asolid-state, gas, or ion medium, and the conditioning optics may includelenses, mirrors, prisms, birefringent filters, and the like. It shouldbe understood, however, that any type of gain medium and conditioningoptics may be used. Also, the gaps shown in FIG. 10 between theindividual components within the laser cavity 200 may or may not beemployed. The function of the VBG 202 may be spectral, spatial, ortemporal conditioning of the laser output.

FIG. 11 provides plots showing how a VBG element can force a laser tooperate on a single longitudinal mode. As an example, a VBG element maybe used as a partially reflective output coupler. The VBG element has anarrow wavelength reflectivity, considerably narrower than the width ofthe gain curve of the active medium of the laser. In order to lase, theindividual longitudinal modes of the laser resonator have to exceed thelasing threshold. Due to the highly selective reflectivity of a VBGoutput coupler, however, only one longitudinal mode of the laser cavityhas a gain exceeding the lasing threshold.

FIGS. 12A and 12B depict a VBG element used as a distributed feedbackelement of a solid-state laser. As shown in FIG. 12A, the VBG element210 can serve as both the active medium and the feedback element. Asshown in FIG. 12B, the VBG element 212 can be attached via an opticalcontact (e.g., fused) to the active medium 214. The resonator mode canbe formed by either the VBG element itself or some additional elements.Both configurations can be used in free-space or waveguide applications.

Similar to narrow wavelength pass-band, a VBG element may have a narrowangle pass-band, as shown in FIG. 13. Preferably, the angular passbandof the VBG element should be wider than the angular width of the TEM₀₀mode of the laser cavity. Due to the relatively sharp roll-off of thediffraction efficiency of a VBG element with angle of incidence (thelaser wavelength is fixed), a higher mode of the laser cavity willexperience higher losses and, therefore, will be essentially suppressedby the VBG element. The VBG element thus functions to strip the laserfrom its higher spatial modes and force it to operate on the TEM₀₀ modeonly.

As shown in FIGS. 14A and 14B, the VBG element has a high diffractionefficiency for the TEM₀₀ mode only and produces higher loss for thehigher spatial modes. The drawing on the right shows an embodiment ofhow it can be used in a laser cavity, comprising at least one mirror224, a gain medium 222, and a VBG element 220 functioning as an outputcoupler. The VBG element 220 may have high reflectivity, and, therefore,low losses, only for the TEM₀₀ mode.

By contrast, as shown in FIGS. 14C and 14D, the VBG element 230 may havea diffraction efficiency profile with a dip at nearly normal incidence,both in azimuth and elevation angle profile. Therefore, it will have lowloss for the TEM₀₀ mode in transmission. Such a VBG element 230 may beused as an essentially transparent (i.e., lossless) element inside thelaser cavity, which may include at least one mirror 234 and a gainmedium 232. Feedback may be provided by a conventional output coupler236, for example, or by a VBG output coupler with angular diffractionefficiency profile as is shown in FIG. 14A.

In the embodiment shown in FIG. 14D, the higher spatial modes willexperience diffraction on the VBG element 230 and, therefore, will bedirected out of the cavity, producing higher losses for those modes and,therefore, eliminating them. In either case the result is TEM₀₀ outputof the laser. VBG elements of both transmission and reflection type canbe used to achieve TEM₀₀ operation. The embodiments depicted in FIGS.14B and 14D are of the so-called “non-folding” type.

FIG. 15 shows a concept for using a reflective VBG element with smoothlyvarying reflectivity profile (“soft aperture”) for inducingsimultaneously single longitudinal mode operation of a laser as well asTEM₀₀-only operation. The VBG element 232 depicted in FIG. 15 functionsas the output coupler of the laser cavity 230, and is axially symmetricaround the resonator axis Z. The laser cavity 230 may include ahigh-reflectivity mirror 236 and a gain medium 234.

FIG. 16 depicts an embodiment suitable for shaping the temporal profileof ultra-short laser pulses. In this embodiment, a VBG element 240 maybe used inside a laser cavity having at least one mirror 246, a gainmedium 244, and other optics 242 (such as lenses, prisms, gratings, andthe like). It is known that ultra-short laser pulses (e.g., <10 psduration) have wide spectral range and will, therefore, likelyexperience dispersion inside the gain medium. The gain medium may bebulk solid-state, fiber, planar waveguide or any other. Such dispersionis generally undesirable because it leads to broadening of theultra-short laser pulse. In accordance with an aspect of the invention,the VBG element 240 may be manufactured with a grating period thatvaries slightly along the axis, z, of the laser. Such a grating mayproduce slightly different delays for different wavelengths and,therefore, will compensate for the dispersion of the gain medium 244 ofthe laser. This improves the temporal characteristics of the laserpulse. Alternatively, the same technique may be used for compression ofthe chirped and stretched high peak power ultra-short pulses subsequentto their amplification in an optical amplifier. The pulses must bestretched prior to the amplification to avoid damage to the amplifier aswell as nonlinear effects.

FIGS. 17A-C depict a VBG element used to construct tunable devices. Asshown in FIGS. 17A and 17B, light emerging from the cavity of an emitter250 may be collimated by a lens 252, if necessary, and incident upon aVBG element 254/264. FIG. 17A shows an embodiment using areflective-type VBG element 254; FIG. 17B shows an embodiment using atransmissive-type VBG element 256. The VBG element 254/264 reflects ordeflects the incident light at an angle onto a folding mirror/reflector256. The folding mirror 256 may then redirect the light to aretro-reflector 258, which reflects the light back on its path. Thelight retraces it path back into the cavity of the emitter 250, forcingthe emitter 250 to operate at the peak wavelength of the VBG filter.Since the peak wavelength of a VBG element 254/264 depends on theincident angle, rotation of the VBG/folding reflector assemblycontinuously tunes the emitted wavelength of light.

As shown in FIG. 17C, light emerging from the cavity of an emitter 270may be collimated by a lens 272, if necessary, and incident upon a VBGelement 274. The VBG element 274 may have a period and peak wavelengththat vary smoothly and continuously as a function of position across itsclear aperture. Thus, the device may include a transverse chirp VBGreflector. When such a VBG element is translated across the output beamof the laser the wavelength of the laser emission will change to followthat of the particular location on the VBG element 274. It should beunderstood that, in the absence of an emitter, the VBG element (plusauxiliary optics) shown in FIGS. 17A - 17C may function as a tunablefilter.

FIGS. 18A and 18B depict spectral/spatial conditioning of an array ofemitters with simultaneous wavelength combining/multiplexing. The lightemitted by each of the emitters in the array 284 is depicted goingthough a particular channel in a wavelength multiplexer 282 positionedin the optical path of light emitted by the array 284. The multiplexer282 combines all different wavelength channels 286 into one outputchannel. The multiplexed light is partially reflected by aretro-reflecting device 280 and the reflected portion of the lightretraces its path back into the different emitters in the array 284. Asa result, each emitter in the array 284 receives wavelength-selectivefeedback and, therefore, will be forced to operate at the wavelength ofthe multiplexer channel 286 it is coupled to. Efficient spectral andspatial conditioning can be achieved in this way with simultaneouscombining of the output of all the emitters in the array. FIG. 18Bdepicts an embodiment where such a multiplexer 282 is constructed of amonolithic glass chip with wavelength-specific VBG nodes 288 recorded inits bulk.

FIG. 19 provides a comparison of the output spectrums of free-runningand VBG-locked, single-emitter lasers. The laser diode parameters were:2 mm cavity length, 1×100 μm emitting aperture, and approximately 0.5%front facet reflectivity. The VBG parameters were: approximately 30%maximum reflectivity, and 0.84 mm thickness. Shown in the inset is acomparison of the output spectrums of free-running and VBG-locked laserdiode bars. The laser bar parameters were: 19 emitters, 1×150 μmemitting aperture for each emitter, and approximately 17% front facetreflectivity. The VBG parameters were: approximately 60% maximumreflectivity, and 0.9 mm thickness.

FIG. 20 provides plots of output power vs. current for a single-emitterlaser diode under different conditions. The laser diode and the VBGparameters were the same as those described in connection with FIG. 19.The inset provides plots of emission spectra of the laser diode atdifferent currents when free-running and locked by the VBG.

FIG. 21 provides plots of emission wavelength of a single-emitter laserdiode as a function of the heatsink temperature when free running w/oFAC lens (circles) and locked by a VBG (squares). Drive current was 1.5A in both cases. The VBG element was attached to the laser heatsinkduring the experiment. Shown in the inset is a plot of output power of alocked laser diode (squares) and a fast-axis collimated laser diode(circles) as a function of its heatsink temperature.

FIG. 22 provides plots that demonstrate the effect of VBG locking on thedivergence of the slow axis of a single-emitter laser diode. The dottedcurve shows the calculated far-field pattern of the light diffracted onthe exit aperture of the laser diode.

FIGS. 23A and 23B depict extra-cavity doubling of a high-power laserdiode frequency. As shown in FIG. 23A, light emitted by a laser diode302 with a high-reflectivity (HR) coating on the back facet and ananti-reflection (AR) coating on the front facet is collimated by a lens304 and is incident upon a VBG element 306. The VBG element 306 reflectsa certain amount of light in a narrow spectral region. The reflectedlight is directed back into the cavity of the laser diode 302, thuslocking the frequency of the laser emission to that of the peakreflectivity of the VBG element 306. The VBG element 306 also narrowsthe emission bandwidth of the laser 302, making it equal to or smallerthan the acceptance bandwidth of the quasi-phase-matched (QPM) nonlinearcrystal 310. The nonlinear crystal 310 is periodically poled to achieveQPM. The light that passes through the VBG element 306 may be focusedinto the QPM crystal 310 by a lens 308. The QPM crystal 310 generatesthe second harmonic of the light emitted by the laser diode 302. The QPMcrystal 310 preferably has AR coating for the fundamental and the secondharmonic on both facets. Light out of the QPM crystal 310 may beredirected through another lens 312.

As shown in FIG. 23B, the VBG element 326 locks the frequency andnarrows the emission spectrum of the laser diode 322. The laser diode322 may have the same characteristics as described above in connectionwith FIG. 23A. The emitted light is focused into a QPM nonlinearwaveguide 330, which generates the second harmonic of the incidentlight. The QPM nonlinear waveguide 330 preferably has AR coating for thefundamental and the second harmonic on both facets. Lenses 324, 328, and332 may be provided as desired.

FIGS. 24A-C depict extra-cavity doubling of a high-power laser diodefrequency. Light emitted through the back facet by a laser diode 344with AR coating on both facets is collimated by a lens 342 and isincident upon a VBG element 340. The VBG element 340 reflects most ofthe light in a narrow spectral region. The reflected light is directedback into the laser cavity, thus forming an external cavity and lockingthe frequency of the laser emission to that of the peak reflectivity ofthe VBG element 340. The front facet of the laser 344 should have enoughreflectivity for the laser 344 to operate above threshold and at adesired output power level. The VBG element 340 also narrows theemission bandwidth of the laser 344, making it equal to or smaller thanthe acceptance bandwidth of the quasi-phase-matched (QPM) nonlinearcrystal 348. A lens 346 may be used to focus the light into the QPMcrystal 348, which then generates the second harmonic of the incidentlight. The QPM crystal 348 preferably has AR coating for the fundamentaland the second harmonic on both facets. A lens 349 may be used to focusthe light output from the QPM crystal.

As shown in FIG. 24B, the light emitted by the laser diode 344 may befocused into a QPM nonlinear waveguide 358, via a lens 356. Thewaveguide 358 may generate the second harmonic of the incident light.The QPM nonlinear waveguide 358 preferably has AR coating for thefundamental and the second harmonic on both facets. As shown in FIG.24C, the QPM nonlinear waveguide 358 abuts the laser diode 344 so thatmost of the light emitted by the laser diode 344 is coupled into the QPMwaveguide 358.

FIGS. 25A and 25B depict intra-cavity doubling of a high-power laserdiode frequency. FIG. 25A depicts a high-power laser diode 370 having HRcoating on the back facet and very low reflectivity AR coating on thefront facet. The external cavity of the laser diode 370 may be formed bya VBG element 371 positioned after a collimating lens 379. A QPM crystal378 may be placed between the VBG element 371 and the front facet of thelaser diode 370, and between a lens pair 376, 379 that focuses the lightinto the QPM crystal 378. By having the QPM crystal 378 positionedinside the external cavity of the laser diode 370, the power of thefundamental harmonic of the laser diode 370 can be increased, thusincreasing the conversion efficiency from the fundamental to the secondharmonic. A window 374 with AR coating for the fundamental harmonic andHR coating for the second harmonic can be placed between the front facetof the laser diode 370 and the QPM crystal 378 in order to increase thetotal power of the second harmonic emitted by this device. The QPMcrystal 378 preferably has AR coating for the fundamental and the secondharmonic on both facets.

As shown in FIG. 25B, the laser diode 370 may abut a QPM nonlinearwaveguide 388. Preferably, the waveguide 388 has AR coating for thefundamental harmonic of light emitted by the laser diode 370 and HRcoating for the second harmonic on its front facet (i.e., the one facingthe laser diode 370). The back facet of the QPM nonlinear waveguide 388preferably has AR coating for both the fundamental and the secondharmonic.

Thus, there have been described example embodiments of apparatus andmethods for conditioning laser characteristics using volume Bragggrating elements. It will be appreciated that modifications may be madeto the disclosed embodiments without departing from the spirit of theinvention. The scope of protection, therefore, is defined by thefollowing claims.

1. A Bragg grating element comprising a photorefractive material havinga holographic Bragg grating recorded therein, said holographic Bragggrating having a grating period that varies continuously as a functionof position along an axis of the Bragg grating element, said Bragggrating defining an entrance aperture and an exit aperture, wherein theentrance aperture and exit aperture coincide.
 2. The Bragg gratingelement of claim 1, wherein the Bragg grating has a longitudinal axis,and the grating period varies as a function of position along thelongitudinal axis.
 3. The Bragg grating element of claim 2, wherein thegrating period varies as a periodic function of position along thelongitudinal axis.
 4. The Bragg grating element of claim 2, wherein thegrating period varies linearly as a function of position along thelongitudinal axis.
 5. The Bragg grating element of claim 2, wherein thelongitudinal axis is an axis along which light received by the Bragggrating is transmitted through the Bragg grating element.
 6. The Bragggrating element of claim 1, wherein the Bragg grating element has alongitudinal axis, and the grating period varies as a function ofposition along an axis that is transverse to the longitudinal axis. 7.The Bragg grating element of claim 6, wherein the grating period variesas a periodic function of position along the transverse axis.
 8. TheBragg grating element of claim 6, wherein the grating period varieslinearly as a function of position along the transverse axis.
 9. TheBragg grating element of claim 6, wherein the longitudinal axis is anaxis along which light received by the Bragg grating is transmittedthrough the Bragg grating element.
 10. The Bragg grating element ofclaim 1, wherein the Bragg grating has a Gaussian reflectivity profile.11. The Bragg grating element of claim 1, wherein the Bragg grating hasa super-Gaussian reflectivity profile.
 12. The Bragg grating element ofclaim 1, wherein the Bragg grating has an axially symmetric reflectivityprofile.
 13. A three-dimensional optical element having a Bragg gratingrecorded therein, said Bragg grating having a reflectivity profile thatvaries continuously as a function of position within the opticalelement, said Bragg grating defining an entrance aperture and an exitaperture, wherein the entrance aperture and exit aperture coincide. 14.The optical element of claim 13, wherein the reflectivity profile is alinear function of position within the optical element.
 15. The opticalelement of claim 13, wherein the reflectivity profile is a Gaussianreflectivity profile.
 16. The optical element of claim 13, wherein thereflectivity profile is a super-Gaussian reflectivity profile.
 17. Theoptical element of claim 13, wherein the reflectivity profile is anaxially symmetric reflectivity profile.
 18. The optical element of claim13, wherein the Bragg grating is a holographic Bragg grating recorded ona photorefractive material.
 19. The Bragg grating element of claim 1,wherein the photorefractive material is a photorefractive glass.
 20. Theoptical element of claim 13, wherein the Bragg grating is recorded in athree-dimensional bulk of photorefractive glass.